Question: Solve for $x$ and $y$ using elimination. ${x+2y = 17}$ ${-x+3y = 3}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $5y = 20$ $\dfrac{5y}{{5}} = \dfrac{20}{{5}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x+2y = 17}\thinspace$ to find $x$ ${x + 2}{(4)}{= 17}$ $x+8 = 17$ $x+8{-8} = 17{-8}$ ${x = 9}$ You can also plug ${y = 4}$ into $\thinspace {-x+3y = 3}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(4)}{= 3}$ ${x = 9}$